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Review total electrical resistance for circuit with two resistors in parallel

abstract:
reference: http://www.dfcd.net/articles/derivations/resistors.html

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 $V = I R$	5258419993 $R_1$ 7191277455 $R$ 1323602089 $I_1$ 2867848403 $I$	4128500715 $V = I_1 R_1$	LHS diff is 0 RHS diff is -pdg0003978pdg0008697 + pdg0004501pdg0006458
2	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 $V = I R$	9746066299 $R_2$ 1377431959 $R$ 5463275819 $I_2$ 5585739998 $I$	9243879541 $V = I_2 R_2$	LHS diff is 0 RHS diff is -pdg0003461pdg0004856 + pdg0004501pdg0006458
3	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	9243879541 $V = I_2 R_2$	3031116098 $R_2$	7002609475 $\frac{V}{R_2} = I_2$	valid
4	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	4128500715 $V = I_1 R_1$	5181421075 $R_1$	2051901211 $\frac{V}{R_1} = I_1$	valid
Note about step 5: current flows through both resistors
5	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			6753224061 $I_{\rm total} = I_1 + I_2$	no validation is available for declarations
6	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 $V = I R$	7410124465 $R_{\rm total}$ 1100332145 $R$ 7798615279 $I_{\rm total}$ 9053099840 $I$	2271186630 $V = I_{\rm total} R_{\rm total}$	LHS diff is 0 RHS diff is -pdg0001908pdg0009647 + pdg0004501pdg0006458
7	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	2271186630 $V = I_{\rm total} R_{\rm total}$	6546594355 $R_{\rm total}$	2809345867 $\frac{V}{R_{\rm total}} = I_{\rm total}$	valid
8	0000111246: substitute LHS of three expressions into expression number of inputs: 4; feeds: 0; outputs: 1 Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} and LHS of Eq.~\ref{eq:#3} into Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}.	6753224061 $I_{\rm total} = I_1 + I_2$ 7002609475 $\frac{V}{R_2} = I_2$ 2051901211 $\frac{V}{R_1} = I_1$ 2809345867 $\frac{V}{R_{\rm total}} = I_{\rm total}$		4866160902 $\frac{V}{R_{\rm total}} = \frac{V}{R_1} + \frac{V}{R_2}$	recognized infrule but not yet supported
9	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	4866160902 $\frac{V}{R_{\rm total}} = \frac{V}{R_1} + \frac{V}{R_2}$	3433441359 $V$	1457415749 $\frac{1}{R_{\rm total}} = \frac{1}{R_1} + \frac{1}{R_2}$	valid
10	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	1457415749 $\frac{1}{R_{\rm total}} = \frac{1}{R_1} + \frac{1}{R_2}$			no validation is available for declarations

Symbols used in total electrical resistance for circuit with two resistors in parallel

0000004501: $ I $
0000003978: $ I_1 $
0000004856: $ I_2 $
0000009647: $ I_{\rm total} $
0000006458: $ R $
0000008697: $ R_1 $
0000003461: $ R_2 $
0000001908: $ R_{\rm total} $
0000006599: $ V $

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0.003 seconds for pdg_app/to_review_derivation 73a7c3ed-e34c-4fed-af2d-e140072a0724
0.003 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivation21a13254-59d6-4011-bd41-042f689d5d05
0.006 seconds for compute/input_feed_output_infrule_for_step: get_inference_rule_connected_to_step_ID21a13254-59d6-4011-bd41-042f689d5d05
0.006 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type HAS_INPUT21a13254-59d6-4011-bd41-042f689d5d05
0.005 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_FEED21a13254-59d6-4011-bd41-042f689d5d05
0.005 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_OUTPUT21a13254-59d6-4011-bd41-042f689d5d05
0.005 seconds for compute/get_dict_of_steps_in_derivation: get_sequence_index_for_step21a13254-59d6-4011-bd41-042f689d5d05
0.004 seconds for pdg_app/ 73a7c3ed-e34c-4fed-af2d-e140072a0724

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 \(V = I R\)	5258419993 \(R_1\) 7191277455 \(R\) 1323602089 \(I_1\) 2867848403 \(I\)	4128500715 \(V = I_1 R_1\)	LHS diff is 0 RHS diff is -pdg0003978pdg0008697 + pdg0004501pdg0006458
2	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 \(V = I R\)	9746066299 \(R_2\) 1377431959 \(R\) 5463275819 \(I_2\) 5585739998 \(I\)	9243879541 \(V = I_2 R_2\)	LHS diff is 0 RHS diff is -pdg0003461pdg0004856 + pdg0004501pdg0006458
3	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	9243879541 \(V = I_2 R_2\)	3031116098 \(R_2\)	7002609475 \(\frac{V}{R_2} = I_2\)	valid
4	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	4128500715 \(V = I_1 R_1\)	5181421075 \(R_1\)	2051901211 \(\frac{V}{R_1} = I_1\)	valid
Note about step 5: current flows through both resistors
5	0000111981: declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an initial equation.			6753224061 \(I_{\rm total} = I_1 + I_2\)	no validation is available for declarations
6	0000111984: change two variables in expression number of inputs: 1; feeds: 4; outputs: 1 Change variable $#1$ to $#2$ and $#3$ to $#4$ in Eq.~\ref{eq:#5}; yields Eq.~\ref{eq:#6}.	4087145886 \(V = I R\)	7410124465 \(R_{\rm total}\) 1100332145 \(R\) 7798615279 \(I_{\rm total}\) 9053099840 \(I\)	2271186630 \(V = I_{\rm total} R_{\rm total}\)	LHS diff is 0 RHS diff is -pdg0001908pdg0009647 + pdg0004501pdg0006458
7	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	2271186630 \(V = I_{\rm total} R_{\rm total}\)	6546594355 \(R_{\rm total}\)	2809345867 \(\frac{V}{R_{\rm total}} = I_{\rm total}\)	valid
8	0000111246: substitute LHS of three expressions into expression number of inputs: 4; feeds: 0; outputs: 1 Substitute LHS of Eq.~\ref{eq:#1} and LHS of Eq.~\ref{eq:#2} and LHS of Eq.~\ref{eq:#3} into Eq.~\ref{eq:#4}; yields Eq.~\ref{eq:#5}.	6753224061 \(I_{\rm total} = I_1 + I_2\) 7002609475 \(\frac{V}{R_2} = I_2\) 2051901211 \(\frac{V}{R_1} = I_1\) 2809345867 \(\frac{V}{R_{\rm total}} = I_{\rm total}\)		4866160902 \(\frac{V}{R_{\rm total}} = \frac{V}{R_1} + \frac{V}{R_2}\)	recognized infrule but not yet supported
9	0000111975: divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.	4866160902 \(\frac{V}{R_{\rm total}} = \frac{V}{R_1} + \frac{V}{R_2}\)	3433441359 \(V\)	1457415749 \(\frac{1}{R_{\rm total}} = \frac{1}{R_1} + \frac{1}{R_2}\)	valid
10	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	1457415749 \(\frac{1}{R_{\rm total}} = \frac{1}{R_1} + \frac{1}{R_2}\)			no validation is available for declarations